In a vehicle including an engine and a multi-speed transmission having any gear position established out of a plurality of gear positions by engaging predetermined engagement devices out of a plurality of engagement devices, a vehicle control device is well known that controls release of a release-side engagement device (the engagement device to be released) of the plurality of engagement devices and engagement of an engagement-side engagement device (the engagement device to be engaged) of the plurality of engagement devices so as to switch the gear position established in the multi-speed transmission (i.e., perform a clutch-to-clutch shift in the multi-speed transmission). For example, this corresponds to a shift control device of a vehicle automatic transmission described in Patent Document 1. In Patent Document 1, it is disclosed that in a coast downshift accompanied with a clutch-to-clutch shift, an occurrence of a tie-up state during the clutch-to-clutch shift is determined based on a racing amount of a turbine rotation speed (i.e., an input rotation speed of the automatic transmission) so as to correct an engagement pressure of the engagement-side engagement device through learning (learning control) in accordance with the tie-up state.